We know that Router can't be used for converting different model (e.g OSI model to TCP/IP or TCP/IP model to OSI) of network. It isn't a multiprotocol converter. But gateway is a highly sophisticated router which can be used for connecting different model of network. I have been finding actual reason behind this but failed to find any fruitful stuff. Can anybody help to make out above concepts.
Models are models - concepts for thought. Like philosophies - sometimes one fits better, some other time the other one.
Converting between TCP/IP model and OSI model doesn't make sense. It's like trying to convert a glass that's half full to a glass that's half empty. It's only a matter of perspective.
The OSI and TCP/IP models are actually very similar. OSI is more detailed (and more theoretical), and TCP/IP focuses on the network (OSI)/internet (IP) and the transport layer, naturally. OSI splits IP's application layer into application, presentation and session (not too common in real life), and IP's link layer is represented by OSI's data link and physical layers (very useful in practice).
On the network layer, router and gateway are the very same thing. There are various feature levels (concerning filtering, firewalling, inspection, address translation, ...) but both terms are interchangeable still.
Gateway can also refer to various other concepts that connect different realms. Gateways from different OSI layers (bridges, routers, proxies, application-layer gateways, ...) are generally different, but even gateways working in the same layer can be vastly different.
Higher-layer gateways can even be used to translate between protocols with a similar purpose, like an FTP-over-HTTP proxy. But all that is off-topic here for working above the transport layer.
I would dare say that you are the victim of the simplistic view presented by network 101 (introduction to networking) courses.
Let me start by quoting from ISO 7498 (the OSI reference model).
The purpose of this Reference Model of Open Systems Interconnection is to provide a common basis for the coordination of standards development for the purpose of systems interconnection, while allowing existing standards to be placed into perspective within the overall Reference Model.
Therefore, it's not a technology, nor is it an architecture, but a reference against which to build and compare architectures.
I would continue by pointing out that gateway and router have been used interchangeably. RFC 791, the original RFC behind IP, defines the gateway as follows:
Gateways implement internet protocol to forward datagrams between networks. Gateways also implement the Gateway to Gateway Protocol (GGP)  to coordinate routing and other internet control information.
Today, gateway is too overloaded to have any real meaning, without a full context being given. On the other hand, the term router has a sharper profile. Primarily, it is an IP packet switch, that switches a packet from an ingress port to an egress port according to the rules it has gathered into the forwarding information base (FIB). Traditionally, and still widely valid, the source of the rules is the data exchanged through the use of a routing protocol and processed by a routing algorithm. The result of the processing is stored in a routing information base (RIB). The router selects a specific entry from the RIB, according to configured criteria, for inclusion in the FIB.
To give one example of the use of gateway, there is an application-level gateway (ALG) used in network address and port translation (NAPT). The ALG inspects the protocol data unit (PDU) relevant to the application (e.g. active FTP) and converts private address information embedded in the PDU into public address information, to enable the function of FTP applications across a NAPT device.